Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-08T05:36:55.619Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of surfactant on bursting gas bubbles

Published online by Cambridge University Press:  26 April 2006

Jeremy M. Boulton-Stone
Jeremy M. Boulton-Stone
Affiliation:
School of Mathemetics and Statistics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical technique, based on the boundary integral method, is developed to allow the modelling of unsteady free-surface flows at large Reynolds numbers in cases where the surface is contaminated by some surface-active compound. This requires the method to take account of the tangential stress condition at the interface and is achieved through a boundary-layer analysis. The constitutive relation that forms the surface stress condition is assumed to be of the Boussinesq type and allows the incorporation of surface shear and dilatational viscous forces as well as Marangoni effects due to gradients in surface tension. Sorption kinetics can be included in the model, allowing calculations for both soluble and insolube surfactants. Application of the numerical model to the problem of bursting gas bubbles at a free surface shows the greatest effect to be due to surface dilatational viscosity which drastically reduces the amount of surface compression and can slow and even prevent the information of a liquid jet. Surface tension gradients give dilatational elasticity to the surface and thus also significantly prevent surface compression. Surface shear viscosity has a smaller effect on the interface motion but results in initially increased surface concentrations due to the sweeping up of surface particles ahead of the inward-moving surface wave.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 231 - 257
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adamson, A. W. 1982, Physical Chemistry of Surfaces. Willey-Interscience.
Avramidis, K. S. & Jiang, T. S., 1991 Measurment of the surface dilatational viscosity of aqueous gelatin-srfactant solutions.. J. Colloid Interface Sci. 147, 262–273.Google Scholar
Blake, J. R., Taib, B. B. & Doherty, G., 1986 Transient cavities near boundaries, Part 1. Rigid boundary.. J. Fluid Mech. 170, 479–497.Google Scholar
Blake, J. R., Taib, B. B. & Doherty, G., 1987 Transient cavities near boundaries, Part 1I. Free Surface. J. Fluid Mech. 181, 197–212.Google Scholar
Boulton-Stone, J. M. & Blake, J. R., 1993, Gas bubbles bursting at a free surface. J. Fluid Mech. 254, 437–466 (referred to herein as BSB).Google Scholar
Garcia-Briones, M. A. & Chalmers, J. J., 1993, Analysis of hydrodynamic information obtained from computer solutions of the rapture of a gas bubble in relation to animal cell damage in sparged bioreactors. In Bioreactor and Bioprocess Fluid Dynamics (ed. A. W. Nienow), pp. 191–210. Mechanical Engineering Publications.
Garcia-Briones, M. A. & Chalmers, J. J., 1994 Flow parameters associate with hydrodynamic cell injury.. Biotech Bioengng 44, 1089–1098.Google Scholar
Garner, F. H., Ellis, S. R. M. & Lacey, J. A. 1954 The size distribution and entrainment of droplets. Trans. Inst. Chem. Engrs 32, 222–235.Google Scholar
Gaver, D. P. & Grtberg, J. B. 1990 The dynamics of a localized surfactant on a thin film. J. Fluid Mech. 213, 127–148.Google Scholar
Gerri, L., Lucca, G. & Prospereitl, A. 1981 A numerical method for the dynamics of non-spherical cavitation bubbles. Proc. 2nd Intl Colloq. On Drops and bubbles, California pp. 175–181.
Harper, J. F. 1972 The motion of bubbles and drops through liquids.. Adv. Appl. Mech. 12. 59 129.Google Scholar
Harper, J. F. 1973 On bubbles with small immobile adsorbed films rising in liquids at low Reynolds numbers. J. Fluid Mech. 58, 539–545.Google Scholar
Harper, J. F. 1974 On spherical bubbles rising steadily in dilute surfactant solutions.. Q. J. Mech. Appl. Maths 27. 87–100.Google Scholar
Harper, J. F. 1988 The rear signation region of abubble rising stadily in a dilute surfactant solution.. Q. J. Mech. Appl. Maths 41, 203–213.Google Scholar
Jensen, O. E. & Grotberg, J. B. 1992 Insoluble surfactant spreading on a thin viscous film: shock evolution and film rupture. J. Fluid Mech. 240, 259–288.Google Scholar
Jensen, O. E. & Grotberg, J. B. 1993 The spreading of heat or soluble surfactant along a thin liquid film.. Phys. Fluids A 5, 58 68.Google Scholar
Johnson, D. O. & Stere, K. J. 1994 Oscillating bubble tensiometry: A method for measuring surfactant adsorptive-desorptive kinctics and surface dilatational viscosity.. J. Colloid Interface Sci. 168. 21–31.Google Scholar
Lemaire, C. & Langevin, D. 1992 Longtudinal surface waves at liquid interfaces: Measurnent of monolayer viscoclasticity. Colloid Surf. 65, 101–112.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall, New Jersey.
Lin, S. Y., Mckeigue, K. & Maldarelli, C. 1991 Diffusion-limited interpretation of the induction period in the relaxation in surface-tension due to the adsorption of of straight chain, small polar group surfactants: Theory and experiments. Langmuir 7, 1055–1066.Google Scholar
Lucassen, J. & Tempel, M. VAN DEN 1972 Longtudinal waves on visco-elastic surfaces. J. Colloid Interface Sci. 41, 491–498.Google Scholar
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects.. J. Fluid Mech 194 479–510.Google Scholar
Moore, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161–176.Google Scholar
Nadim, A., Kumar, S. & Greenspan, H. P. 1993 Boundary integral calculations of bubble dynamics in the presence of surfactants. Talk given at Am. Phys. Soc. Fluid Dynamics Division meeting, New Mexico.
Newitt, D. M., Dombrowski, N. & Knelman, F. H. 1954 Liquid entrainment 1. the mechanism of drop formation from gas or vapour bubbles. Trans. Inst. Chem. Engrs 32, 244–261.Google Scholar
Sadiial, S. S. & Johnson, R. F. 1983 Stokes flow past bubbles and drops partially coated with thin flims. Part 1 Stagnant cap of surfactant film exact solution. J. Fluid Mech. 126, 237–250.Google Scholar
Savic, P. 1953 Circulation and distortion of liquid drops falling though a viscous medium. Nat. Res. Counc. Can. Div. Mech. Engng Rep. MT 22.
Slattery, J. C. 1990 Interfacial Transport Phenomena. Apringer-Verlag, New York.
Taib, B. B. 1985 Boundary element method applied to cavitation bubble dynamics. PhD thesis, University of Wollongong Australia.